Computer firm HP has also donated $1 million to help the cause, which will involve piloting new technology tools for the children to use for their education.
The couple set up the foundation in late 2016 to "advance justice in courtrooms, communities, and classrooms around the world".
The couple's foundation is partnering with UNICEF to fund seven public schools in Lebanon and help some 3,000 refugee students now not attending school.
The Clooney Foundation for Justice just announced a $2.25 million partnership with UNICEF to fund seven schools in Lebanon to help 3,000 now out-of-school refugee schoolkids.
A spokesman for the Clooneys' foundation, Max Gleischman, said the organisation had made a decision to support education for Syrian refugees through the public school system, instead of investing in private schools operated by Sabis, an worldwide company which has prepared students for college and high school exams. "Formal education can help change that", the couple said in a statement. "That's our goal with this initiative".
"We do not want to lose a whole generation because they were born in a wrong era", revealed the legendary actor.
Nearly 500.000 Syrian children have found their salvation in Lebanon and 200.000 still have no access to any education source, according to the United Nations.
Amal Alamuddin and the former "eternal bachelor" tied the knot in 2014 during an intimate ceremony in Venice.